Watford defended well, and were at times were able to put pressure on the home side, though these attempts were ultimately fruitless thanks to some good saves by Petr Cech, searching for his 200th Premier League clean sheet.
And the victory was sealed for Arsenal in the 77th minute, when Henrikh Mkhitaryan fired in a third from the edge of the box for his first Premier League goal for the Gunners. The win moves Arsenal to within 10 points of Tottenham, ahead of their match against Bournemouth later on Sunday.
Deeney questioned Arsenal's attitude after his penalty helped Watford come from behind to beat the Gunners in the reverse fixture in October, but this time they were eventually well-beaten.
The Spanish worldwide was considered a doubt for next week's Europa League second leg but Wenger now claims Bellerin could be back to face Milan on Thursday.
Arsenal saw off Watford to secure their first Premier League win in four games and continue their recovery from a disastrous run of results.
Things got even worse when the 29-year-old striker failed to convert his penalty adding more salt to the wounds which were rubbed in his face by the vocal Arsenal fans in the Emirates stadium as their team won 3-0.
Arsenal FC players celebrate a goal during a match against Watford FC on 11 March 2018.
However, the Englishman feels the north London outfit can have a strong end of the season following two much needed victories.
Cech alertly kept out Richarlison's dipping free-kick, but Roberto Pereyra should have done better than blaze the rebound over.
Aubameyang and Mkhitaryan also had scoring chances in the first half but were both denied by the heroics of Otestis Karnezis in goal for Watford.
The keeper, who also recorded his 200th league clean sheet, looked as surprised as the home fans on a day when thousands stayed at home.
Karnezis could do nothing, however, to prevent Shkodran Mustafi's eighth-minute header, steered into the left of goal from Ozil's left-hand-side free kick.